Home
Class 12
MATHS
Statement-1 : Tangents drawn from the po...

Statement-`1` : Tangents drawn from the point `(2,-1)(2,-1)` to the hyperbola `x^(2)-4y^(2)=4` are at right angle.
Statement-`2` : The locus of the point of intersection of perpendicular tangents to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is the circle `x^(2)+y^(2)=a^(2)-b^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
T
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (2) (FILL IN THE BLANKS) |4 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (3) (MCQ)|8 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (2) (MCQ) |20 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

Similar Questions

Explore conceptually related problems

Statement- 1 : Tangents drawn from the point (2,-1) to the hyperbola x^(2)-4y^(2)=4 are at right angle. Statement- 2 : The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is the circle x^(2)+y^(2)=a^(2)-b^(2) .

The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(3)-(y^(2))/(1)=1 , is

Knowledge Check

  • The locus of the point of intersection of perpendicular tangents to the circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) , is

    A
    `x^(2)+y^(2)=a^(2)-b^(2)`
    B
    `x^(2)+y^(2)=a^(2)+b^(2)`
    C
    `x^(2)+y^(2)=(a+b)^(2)`
    D
    none of these

  • Statement-1: Tangents drawn from any point on the circle x^(2)+y^(2)=25 to the ellipse (x^(2))/(16)+(y^(2))/(9)=1 are at right angle Statement-2: The locus of the point of intersection of perpendicular tangents to an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is its director circle x^(2)+y^(2)=a^(2)+b^(2) .

    A
    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
    B
    Statement-1 is True, Statement-2 is True, Statement -2 is not a correct explanation for Statement-1
    C
    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True

  • the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

    A
    a circle
    B
    a parabola
    C
    an ellipse
    D
    a hyperbola

    • Similar Questions

    Explore conceptually related problems

    Locus of point of intersection of perpendicular tangents to the circle x^(2)+y^(2)-4x-6y-1=0 is

    The locus of the point of intersection of perpendicular tangents to the ellipse (x - 1)^2/16 + (y-2)^2/9= 1 is

    The locus of the point of intersection of two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, If sum of slopes is constant lambda is

    Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

    Locus of point of intersection of two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , the product of whose slopes is c^(2) the curve

    Home
    Profile